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Distribution of Fishes in the Red River of the North Basin on Multivariate Environmental Gradients

Stream Similarity

Cluster analysis

The presence of 76 naturally reproducing stream fish species was recorded in binary (presence or absence) format for each of 27 streams in the Red River basin. To determine similarity of streams, the 76x27 array was used to calculate Jaccard's coefficients (JI) (Ludwig and Reynolds 1988) for each stream pair (A and B), where JI=a/(a+b+c), with a as the number of species that streams A and B have in common, b as the number of species present in stream A but absent from stream B, and c as the number of species present in stream B but absent from stream A. The JI ranged from near 0 (for a stream pair highly dissimilar with respect to fish species) to near 1 (stream pair very similar).

To place streams into meaningful groups, the JI for all combinations of stream pairs were summarized into a 27x27 array or similarity matrix. An agglomerative clustering technique (weighted centroid) provided in the Multivariate Statistical Package (MVSP) of Kovach (1993) was used to produce a dendrogram containing all 27 streams. A minimum JI of 0.0 was used for defining clusters (A-D). Other measures of similarity and also measures of distance between streams were attempted along with several different methods of clustering (single-linkage and complete-linkage techniques). All techniques provided similar results, with the JI and weighted centroid clustering being most meaningful ecologically.

Significance of clusters

To determine if clusters of streams produced in the CA were significantly different from one another, a PCA (Ludwig and Reynolds 1988) was conducted followed by a multiple response permutation procedure (MRPP) (Biondini et al. 1988). The PCA was run using a centered covariance matrix created from the 76x27 binary array using MVSP (Kovach 1993). Component loadings of PCA axes were species, and PCA scores were obtained for each of the 27 streams. An ordination diagram of streams plotted on axes 1 and 2 was produced and compared with results of the CA.

The MRPP is a "distribution-free" permutation technique for the analysis of ecological data which does not require parametric assumptions of normality (Biondini et al. 1988). Input into the MRPP program were 27 observations (streams), with five dimensions (the PCA scores for each stream from the first five axes), in four groups (clusters A-D from CA) of sizes eight, eight, seven, and four. Significance of clusters was determined by examining the P-value produced by MRPP.

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